Besides commemorating the feast of "Mary, Mother of God" on January 1, the Catholic Church traditionally celebrated the "Circumcision of the Lord" on that day. It is the eighth day after the celebration of Jesus' birth and recalls the ancient Hebrew tradition of circumcision that was inaugurated under Abraham.
According to the book of Genesis, God said to Abraham, "This is my covenant, which you shall keep, between me and you and your descendants after you: Every male among you shall be circumcised. You shall be circumcised in the flesh of your foreskins, and it shall be a sign of the covenant between me and you. He that is eight days old among you shall be circumcised; every male throughout your generations ... So shall my covenant be in your flesh an everlasting covenant" (Genesis 17:10-12a,13b).
This covenant ritual was renewed under Joshua and remained in effect up to the time of Jesus (and many Jews still practice this today).
But why did Jesus, Lord of the New Covenant, submit himself to a practice that was part of the "Old Law"?
St. Paul gives us an insight in his letter to the Galatians.
[W]hen the time had fully come, God sent forth his Son, born of woman, born under the law, to redeem those who were under the law, so that we might receive adoption as sons. And because you are sons, God has sent the Spirit of his Son into our hearts, crying, “Abba! Father!” So through God you are no longer a slave but a son, and if a son then an heir.
Jesus was a faithful Jew so that he might renew that which was "old," in order to bring us under a New Covenant in his blood. For this reason, circumcision is no longer a sign of the covenant we have with God, as St. Paul explains later in his letter to the Galatians.
For in Christ Jesus neither circumcision nor uncircumcision is of any avail, but faith working through love.
The ritual was an essential part of Jesus' mission to redeem us and many ancient spiritual writers saw it as a foreshadowing of Christ's bloody sacrifice on the cross. The two events are linked and help us to see the complete picture of Jesus' saving action on earth.
The reason for Jesus' circumcision can be best summed up in the book of Revelation, where Jesus proclaims, "Behold, I make all things new" (Revelation 21:5).